Data Structures with Arithmetic Constraints: A Non-disjoint Combination
Identifieur interne : 000D23 ( Istex/Corpus ); précédent : 000D22; suivant : 000D24Data Structures with Arithmetic Constraints: A Non-disjoint Combination
Auteurs : Enrica Nicolini ; Christophe Ringeissen ; Michaël RusinowitchSource :
- Lecture Notes in Computer Science [ 0302-9743 ]
Abstract
Abstract: We apply an extension of the Nelson-Oppen combination method to develop a decision procedure for the non-disjoint union of theories modeling data structures with a counting operator and fragments of arithmetic. We present some data structures and some fragments of arithmetic for which the combination method is complete and effective. To achieve effectiveness, the combination method relies on particular procedures to compute sets that are representative of all the consequences over the shared theory. We show how to compute these sets by using a superposition calculus for the theories of the considered data structures and various solving and reduction techniques for the fragments of arithmetic we are interested in, including Gauss elimination, Fourier-Motzkin elimination and Groebner bases computation.
Url:
DOI: 10.1007/978-3-642-04222-5_20
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ISTEX:37F97C96FC3787CCA95BB66B88555E480D048508Le document en format XML
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type="institution">University of Bern</orgName><address><settlement>Bern</settlement><country key="CH">SWITZERLAND</country></address></affiliation></editor><editor><persName><forename type="first">C.</forename><surname>Pandu Rangan</surname></persName><affiliation><orgName type="institution">Indian Institute of Technology</orgName><address><settlement>Madras</settlement><country key="IN">INDIA</country></address></affiliation></editor><editor><persName><forename type="first">Bernhard</forename><surname>Steffen</surname></persName><affiliation><orgName type="institution">University of Dortmund</orgName><address><settlement>Dortmund</settlement><country key="DE">GERMANY</country></address></affiliation></editor><editor><persName><forename type="first">Madhu</forename><surname>Sudan</surname></persName><affiliation><orgName type="institution">Massachusetts Institute of Technology</orgName><address><region>MA</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Demetri</forename><surname>Terzopoulos</surname></persName><affiliation><orgName type="institution">University of California</orgName><address><settlement>Los Angeles</settlement><region>CA</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Doug</forename><surname>Tygar</surname></persName><affiliation><orgName type="institution">University of California</orgName><address><settlement>Berkeley</settlement><region>CA</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Moshe</forename><forename type="first">Y.</forename><surname>Vardi</surname></persName><affiliation><orgName type="institution">Rice University</orgName><address><settlement>Houston</settlement><region>TX</region><country key="US">UNITED STATES</country></address></affiliation></editor><editor><persName><forename type="first">Gerhard</forename><surname>Weikum</surname></persName><affiliation><orgName type="institution">Max-Planck Institute of Computer Science</orgName><address><settlement>Saarbrücken</settlement><country key="DE">GERMANY</country></address></affiliation></editor><idno type="pISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="seriesID">558</idno></series></biblStruct></sourceDesc></fileDesc><profileDesc><abstract xml:lang="en"><head>Abstract</head><p>We apply an extension of the Nelson-Oppen combination method to develop a decision procedure for the non-disjoint union of theories modeling data structures with a counting operator and fragments of arithmetic. We present some data structures and some fragments of arithmetic for which the combination method is complete and effective. To achieve effectiveness, the combination method relies on particular procedures to compute sets that are representative of all the consequences over the shared theory. We show how to compute these sets by using a superposition calculus for the theories of the considered data structures and various solving and reduction techniques for the fragments of arithmetic we are interested in, including Gauss elimination, Fourier-Motzkin elimination and Groebner bases computation.</p></abstract><textClass ana="subject"><keywords scheme="book-subject-collection"><list><label>SUCO11645</label><item><term>Computer Science</term></item></list></keywords></textClass><textClass ana="subject"><keywords scheme="book-subject"><list><label>I</label><item><term type="Primary">Computer Science</term></item><label>I21017</label><item><term type="Secondary" subtype="priority-1">Artificial Intelligence (incl. 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Zurich</OrgName><OrgAddress><City>Zurich</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff6"><OrgName>Stanford University</OrgName><OrgAddress><City>Stanford</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff7"><OrgName>Weizmann Institute of Science</OrgName><OrgAddress><City>Rehovot</City><Country>Israel</Country></OrgAddress></Affiliation><Affiliation ID="Aff8"><OrgName>University of Bern</OrgName><OrgAddress><City>Bern</City><Country>Switzerland</Country></OrgAddress></Affiliation><Affiliation ID="Aff9"><OrgName>Indian Institute of Technology</OrgName><OrgAddress><City>Madras</City><Country>India</Country></OrgAddress></Affiliation><Affiliation ID="Aff10"><OrgName>University of Dortmund</OrgName><OrgAddress><City>Dortmund</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff11"><OrgName>Massachusetts Institute of Technology</OrgName><OrgAddress><State>MA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff12"><OrgName>University of California</OrgName><OrgAddress><City>Los Angeles</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff13"><OrgName>University of California</OrgName><OrgAddress><City>Berkeley</City><State>CA</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff14"><OrgName>Rice University</OrgName><OrgAddress><City>Houston</City><State>TX</State><Country>USA</Country></OrgAddress></Affiliation><Affiliation ID="Aff15"><OrgName>Max-Planck Institute of Computer Science</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></SeriesHeader><SubSeries><SubSeriesInfo><SubSeriesID>1244</SubSeriesID><SubSeriesPrintISSN>0302-9743</SubSeriesPrintISSN><SubSeriesElectronicISSN>1611-3349</SubSeriesElectronicISSN><SubSeriesTitle Language="En">Lecture Notes in Artificial Intelligence</SubSeriesTitle></SubSeriesInfo><SubSeriesHeader><EditorGroup><Editor AffiliationIDS="Aff16"><EditorName DisplayOrder="Western"><GivenName>Randy</GivenName><FamilyName>Goebel</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff17"><EditorName DisplayOrder="Western"><GivenName>Jörg</GivenName><FamilyName>Siekmann</FamilyName></EditorName></Editor><Editor AffiliationIDS="Aff18"><EditorName DisplayOrder="Western"><GivenName>Wolfgang</GivenName><FamilyName>Wahlster</FamilyName></EditorName></Editor><Affiliation ID="Aff16"><OrgName>University of Alberta</OrgName><OrgAddress><City>Edmonton</City><Country>Canada</Country></OrgAddress></Affiliation><Affiliation ID="Aff17"><OrgName>University of Saarland</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation><Affiliation ID="Aff18"><OrgName>DFKI and University of Saarland</OrgName><OrgAddress><City>Saarbrücken</City><Country>Germany</Country></OrgAddress></Affiliation></EditorGroup></SubSeriesHeader></SubSeries><Book Language="En"><BookInfo BookProductType="Proceedings" ContainsESM="No" Language="En" MediaType="eBook" NumberingStyle="Unnumbered" OutputMedium="All" TocLevels="0"><BookID>978-3-642-04222-5</BookID><BookTitle>Frontiers of Combining Systems</BookTitle><BookSubTitle>7th International Symposium, FroCoS 2009, Trento, Italy, September 16-18, 2009. Proceedings</BookSubTitle><BookVolumeNumber>5749</BookVolumeNumber><BookSequenceNumber>5749</BookSequenceNumber><BookDOI>10.1007/978-3-642-04222-5</BookDOI><BookTitleID>191175</BookTitleID><BookPrintISBN>978-3-642-04221-8</BookPrintISBN><BookElectronicISBN>978-3-642-04222-5</BookElectronicISBN><BookChapterCount>23</BookChapterCount><BookCopyright><CopyrightHolderName>Springer Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2009</CopyrightYear></BookCopyright><BookSubjectGroup><BookSubject Code="I" Type="Primary">Computer Science</BookSubject><BookSubject Code="I21017" Priority="1" Type="Secondary">Artificial Intelligence (incl. Robotics)</BookSubject><BookSubject Code="I16048" Priority="2" Type="Secondary">Mathematical Logic and Formal Languages</BookSubject><BookSubject Code="I1603X" Priority="3" Type="Secondary">Logics and Meanings of Programs</BookSubject><BookSubject Code="I14029" Priority="4" Type="Secondary">Software Engineering</BookSubject><BookSubject Code="I16021" Priority="5" Type="Secondary">Algorithm Analysis and Problem Complexity</BookSubject><BookSubject Code="I14010" Priority="6" Type="Secondary">Programming Techniques</BookSubject><SubjectCollection Code="SUCO11645">Computer Science</SubjectCollection></BookSubjectGroup><BookContext><SeriesID>558</SeriesID><SubSeriesID>1244</SubSeriesID></BookContext></BookInfo><BookHeader><EditorGroup><Editor AffiliationIDS="Aff19"><EditorName DisplayOrder="Western"><GivenName>Silvio</GivenName><FamilyName>Ghilardi</FamilyName></EditorName><Contact><Email>ghilardi@dsi.unimi.it</Email></Contact></Editor><Editor AffiliationIDS="Aff20"><EditorName DisplayOrder="Western"><GivenName>Roberto</GivenName><FamilyName>Sebastiani</FamilyName></EditorName><Contact><Email>rseba@disi.unitn.it</Email></Contact></Editor><Affiliation ID="Aff19"><OrgDivision>Department of Computer Science</OrgDivision><OrgName>Università degli Studi di Milano</OrgName><OrgAddress><Street>Via Comelico 39</Street><Postcode>20135</Postcode><City>Milano</City><Country>Italy</Country></OrgAddress></Affiliation><Affiliation ID="Aff20"><OrgDivision>Dipartemento di Ingegneria e Scienza dell’Informazione</OrgDivision><OrgName>Università di Trento, Facoltà di Scienze</OrgName><OrgAddress><Street>Via Sommarive 14</Street><Postcode>38050</Postcode><City>Povo</City><State>Trento</State><Country>Italy</Country></OrgAddress></Affiliation></EditorGroup></BookHeader><Part ID="Part2"><PartInfo TocLevels="0"><PartID>2</PartID><PartSequenceNumber>2</PartSequenceNumber><PartTitle>Technical Papers</PartTitle><PartChapterCount>19</PartChapterCount><PartContext><SeriesID>558</SeriesID><BookTitle>Frontiers of Combining Systems</BookTitle></PartContext></PartInfo><Chapter ID="Chap20" Language="En"><ChapterInfo ChapterType="OriginalPaper" ContainsESM="No" NumberingStyle="Unnumbered" TocLevels="0"><ChapterID>20</ChapterID><ChapterDOI>10.1007/978-3-642-04222-5_20</ChapterDOI><ChapterSequenceNumber>20</ChapterSequenceNumber><ChapterTitle Language="En">Data Structures with Arithmetic Constraints: A Non-disjoint Combination</ChapterTitle><ChapterFirstPage>319</ChapterFirstPage><ChapterLastPage>334</ChapterLastPage><ChapterCopyright><CopyrightHolderName>Springer-Verlag Berlin Heidelberg</CopyrightHolderName><CopyrightYear>2009</CopyrightYear></ChapterCopyright><ChapterGrants Type="Regular"><MetadataGrant Grant="OpenAccess"></MetadataGrant><AbstractGrant Grant="OpenAccess"></AbstractGrant><BodyPDFGrant Grant="Restricted"></BodyPDFGrant><BodyHTMLGrant Grant="Restricted"></BodyHTMLGrant><BibliographyGrant Grant="Restricted"></BibliographyGrant><ESMGrant Grant="Restricted"></ESMGrant></ChapterGrants><ChapterContext><SeriesID>558</SeriesID><PartID>2</PartID><BookID>978-3-642-04222-5</BookID><BookTitle>Frontiers of Combining Systems</BookTitle></ChapterContext></ChapterInfo><ChapterHeader><AuthorGroup><Author AffiliationIDS="Aff21"><AuthorName DisplayOrder="Western"><GivenName>Enrica</GivenName><FamilyName>Nicolini</FamilyName></AuthorName><Contact><Email>Enrica.Nicolini@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff21"><AuthorName DisplayOrder="Western"><GivenName>Christophe</GivenName><FamilyName>Ringeissen</FamilyName></AuthorName><Contact><Email>Christophe.Ringeissen@loria.fr</Email></Contact></Author><Author AffiliationIDS="Aff21"><AuthorName DisplayOrder="Western"><GivenName>Michaël</GivenName><FamilyName>Rusinowitch</FamilyName></AuthorName><Contact><Email>Michael.Rusinowitch@loria.fr</Email></Contact></Author><Affiliation ID="Aff21"><OrgName>LORIA & INRIA Nancy Grand Est</OrgName><OrgAddress><Country>France</Country></OrgAddress></Affiliation></AuthorGroup><Abstract ID="Abs1" Language="En"><Heading>Abstract</Heading><Para>We apply an extension of the Nelson-Oppen combination method to develop a decision procedure for the non-disjoint union of theories modeling data structures with a counting operator and fragments of arithmetic. We present some data structures and some fragments of arithmetic for which the combination method is complete and effective. To achieve effectiveness, the combination method relies on particular procedures to compute sets that are representative of all the consequences over the shared theory. We show how to compute these sets by using a superposition calculus for the theories of the considered data structures and various solving and reduction techniques for the fragments of arithmetic we are interested in, including Gauss elimination, Fourier-Motzkin elimination and Groebner bases computation.</Para></Abstract><ArticleNote Type="Misc"><SimplePara>This work is partly funded by the ANR project “DeCert”.</SimplePara></ArticleNote></ChapterHeader><NoBody></NoBody></Chapter></Part></Book></Series></Publisher></istex:document></istex:metadataXml><mods version="3.6"><titleInfo lang="en"><title>Data Structures with Arithmetic Constraints: A Non-disjoint Combination</title></titleInfo><titleInfo type="alternative" contentType="CDATA"><title>Data Structures with Arithmetic Constraints: A Non-disjoint Combination</title></titleInfo><name type="personal"><namePart type="given">Enrica</namePart><namePart type="family">Nicolini</namePart><affiliation>LORIA & INRIA Nancy Grand Est, France</affiliation><affiliation>E-mail: Enrica.Nicolini@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Christophe</namePart><namePart type="family">Ringeissen</namePart><affiliation>LORIA & INRIA Nancy Grand Est, France</affiliation><affiliation>E-mail: Christophe.Ringeissen@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><name type="personal"><namePart type="given">Michaël</namePart><namePart type="family">Rusinowitch</namePart><affiliation>LORIA & INRIA Nancy Grand Est, France</affiliation><affiliation>E-mail: Michael.Rusinowitch@loria.fr</affiliation><role><roleTerm type="text">author</roleTerm></role></name><typeOfResource>text</typeOfResource><genre displayLabel="OriginalPaper" authority="ISTEX" authorityURI="https://content-type.data.istex.fr" type="conference" valueURI="https://content-type.data.istex.fr/ark:/67375/XTP-BFHXPBJJ-3">conference</genre><originInfo><publisher>Springer Berlin Heidelberg</publisher><place><placeTerm type="text">Berlin, Heidelberg</placeTerm></place><dateIssued encoding="w3cdtf">2009</dateIssued><copyrightDate encoding="w3cdtf">2009</copyrightDate></originInfo><language><languageTerm type="code" authority="rfc3066">en</languageTerm><languageTerm type="code" authority="iso639-2b">eng</languageTerm></language><abstract lang="en">Abstract: We apply an extension of the Nelson-Oppen combination method to develop a decision procedure for the non-disjoint union of theories modeling data structures with a counting operator and fragments of arithmetic. We present some data structures and some fragments of arithmetic for which the combination method is complete and effective. To achieve effectiveness, the combination method relies on particular procedures to compute sets that are representative of all the consequences over the shared theory. We show how to compute these sets by using a superposition calculus for the theories of the considered data structures and various solving and reduction techniques for the fragments of arithmetic we are interested in, including Gauss elimination, Fourier-Motzkin elimination and Groebner bases computation.</abstract><relatedItem type="host"><titleInfo><title>Frontiers of Combining Systems</title><subTitle>7th International Symposium, FroCoS 2009, Trento, Italy, September 16-18, 2009. Proceedings</subTitle></titleInfo><name type="personal"><namePart type="given">Silvio</namePart><namePart type="family">Ghilardi</namePart><affiliation>Department of Computer Science, Università degli Studi di Milano, Via Comelico 39, 20135, Milano, Italy</affiliation><affiliation>E-mail: ghilardi@dsi.unimi.it</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Roberto</namePart><namePart type="family">Sebastiani</namePart><affiliation>Dipartemento di Ingegneria e Scienza dell’Informazione, Università di Trento, Facoltà di Scienze, Via Sommarive 14, 38050, Povo, Trento, Italy</affiliation><affiliation>E-mail: rseba@disi.unitn.it</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><genre type="book-series" authority="ISTEX" authorityURI="https://publication-type.data.istex.fr" valueURI="https://publication-type.data.istex.fr/ark:/67375/JMC-0G6R5W5T-Z">book-series</genre><originInfo><publisher>Springer</publisher><copyrightDate encoding="w3cdtf">2009</copyrightDate><issuance>monographic</issuance></originInfo><subject><genre>Book-Subject-Collection</genre><topic authority="SpringerSubjectCodes" authorityURI="SUCO11645">Computer Science</topic></subject><subject><genre>Book-Subject-Group</genre><topic authority="SpringerSubjectCodes" authorityURI="I">Computer Science</topic><topic authority="SpringerSubjectCodes" authorityURI="I21017">Artificial Intelligence (incl. Robotics)</topic><topic authority="SpringerSubjectCodes" authorityURI="I16048">Mathematical Logic and Formal Languages</topic><topic authority="SpringerSubjectCodes" authorityURI="I1603X">Logics and Meanings of Programs</topic><topic authority="SpringerSubjectCodes" authorityURI="I14029">Software Engineering</topic><topic authority="SpringerSubjectCodes" authorityURI="I16021">Algorithm Analysis and Problem Complexity</topic><topic authority="SpringerSubjectCodes" authorityURI="I14010">Programming Techniques</topic></subject><identifier type="DOI">10.1007/978-3-642-04222-5</identifier><identifier type="ISBN">978-3-642-04221-8</identifier><identifier type="eISBN">978-3-642-04222-5</identifier><identifier type="ISSN">0302-9743</identifier><identifier type="eISSN">1611-3349</identifier><identifier type="BookTitleID">191175</identifier><identifier type="BookID">978-3-642-04222-5</identifier><identifier type="BookChapterCount">23</identifier><identifier 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type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Josef</namePart><namePart type="family">Kittler</namePart><affiliation>University of Surrey, Guildford, UK</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Jon</namePart><namePart type="given">M.</namePart><namePart type="family">Kleinberg</namePart><affiliation>Cornell University, Ithaca, NY, USA</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">Friedemann</namePart><namePart type="family">Mattern</namePart><affiliation>ETH Zurich, Zurich, Switzerland</affiliation><role><roleTerm type="text">editor</roleTerm></role></name><name type="personal"><namePart type="given">John</namePart><namePart type="given">C.</namePart><namePart type="family">Mitchell</namePart><affiliation>Stanford University, Stanford, CA, USA</affiliation><role><roleTerm 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